STREAMER DYNAMICS IN A MEDIA CONTAINING DUST PARTICLES*

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STREAMER DYNAMICS IN A MEDIA CONTAINING DUST
PARTICLES Natalia Yu. Babaeva and Mark J.
Kushner Iowa State University Department of
Electrical and Computer Engineering Ames, IA
50011, USA natalie5_at_iastate.edu
mjk_at_iastate.edu
http//uigelz.ece.iastate.edu July 2005
Work supported by the National Science
Foundation and Air Force Research Lab
ICPIG2005_01
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AGENDA

• Streamer dynamics through aerosols and dust
  particles
• Description of the model
• Effect of dust particles on streamer dynamics
• Dynamics before and after particles
• Multiple particles
• Summary

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STREAMER DYNAMICS

• Streamers are ionization waves having a high
  electric field at the avalanche front.
• Air or other gases can be contaminated with
  particles or aerosols having sizes of 10s to
  100s µm.
• The intersection of propagating streamers with
  particles can significantly perturb streamer
  dynamics.

Streamer in atmospheric pressure gases.
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DESCRIPTION OF THE MODEL GEOMETRY

• Positive corona is sustained between between a
  rod (rc 0.07 cm) at 15 kV and a grounded surface
  separated by 0.2 cm.
• 2-d unstructured mesh is produced with Skymesh2.

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DESCRIPTION OF THE MODEL BASIC EQUATIONS

• Poissons equation, continuity equations and
  surface charge are simultaneously solved using a
  Newton iteration technique.

N2/O2/H2O 79.5/19.5/1.0
Species N2, N2(v), N2, N2, N2, N, N,
N, N4, O2, O2, O2, O2-, O-, O, O, O,
O3, H2O, H2O, H2, H, OH, e
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TYPICAL STREAMER PARAMETERS POTENTIAL
15000 V, 0 6 ns

• Potential is compressed in front of the streamer
  head.
• Potential drop inside the streamer is small.
• Streamer is analogous to the metal rod on the
  axis.

ANIMATION SLIDE
t 0 6 ns t 0 6 ns
0 - 15000 (V)
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TYPICAL STREAMER PARAMETERS E/N
15000 V, 0 6 ns

• Electric field is high at the streamer tip where
  ionization occurs.
• Electric field is small in the conducting
  channel.

ANIMATION SLIDE
t 0 6 ns t 0 6 ns
100 1000 (Td) Log scale
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TYPICAL STREAMER PARAMETERS e, CHARGE,
e Space Charge
15000 V, 0 6 ns

• The electron density behind the streamer front is
  1013-1014 cm-3 .
• The plasma in the inner part of the streamer
  channel is quasi-neutral.
• Positive space charge is concentrated at the
  streamer boundary.

Log scale
1010 - 3 x 1014 (cm-3) 1011 - 1013 (cm-3)
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t 5.0 ns
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E/N BEFORE 20, 60 and 80 ?m DUST PARTICLE
15000 V, 0 6 ns
E/N

• Streamer velocity and electric field increase as
  the streamer approaches the particle.

No particle r 20?m r 60?m r
80?m
t 3.8 ns
100 - 1000 (Td) Log scale
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E-FIELD AFTER 80?m PARTICLE
E/N

• The conical streamer head develops into a
  concave tip.
• A new streamer starts from the bottom side facing
  the grounded electrode. The two streamers
  eventually merge.
• If the particle has sharp features , electric
  field enhancement launches a secondary streamer
  that does not merge with the primary streamer.

ANIMATION SLIDE
t 0 5 ns t 0 5.2 ns
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100 - 1000 (Td) Log scale
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E-FIELD AFTER 60?m PARTICLE
E/N

• The conical streamer head develops into a
  concave tip.
• The streamer compresses the E-field field between
  its tip and the particle surface facing the
  front.
• Plasma envelopes smaller particles (20 µm, 60 µm).

t 4.15 t 4.7 t 4.15
t 4.7 ns
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100 - 1000 (Td) Log scale
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SURFACE AND SPACE CHARGE FOR 80?m PARTICLE

• Streamer delivers a substantial positive charge
  to top of particle.
• Charging of particle occurs within 1 ns.
• In a repetitively pulsed system, the charge
  accumulated on a particle can influence
  subsequent streamers.

1012 to 1013 (cm-3) Log scale
t 4.5 ns
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ELECTRIC FIELD NEAR SPHERE IN EXTERNAL E-FIELD

• Solution of Laplaces equation outside a
  conducting particle of radius a in an external
  electric field.

• Near the particle

• E 5000 V/cm

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POTENTIAL DIELECTRIC PARTICLES (r 80?m)
ANIMATION SLIDE
t 0 - 5.2 ns
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100 - 1000 (Td) Log scale
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ELECTRIC FIELD DIELECTRIC PARTICLES (r 80?m)
ANIMATION SLIDE
t 0 5.2 ns
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100 - 1000 (Td) Log scale
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STREAMER INTERACTION TWO PARTICLES (r 80?m)
E/N

• Streamer dynamics for the upper particle are
  similar to a single isolated particle.
• A second streamer is launched from the bottom of
  the first particle. A third streamer is launched
  from the lower surface of the second particle.
• This process is repetitive for particles of the
  same size and evenly spaced.

t 0 5.2 ns
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STREAMER INTERACTION THREE PARTICLES (r 80?m)
E/N

• Launching of secondary and tertiary streamers
  with three particles is the same as for two
  particles.

t 0 5.2 ns
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STREAMER INTERACTION THREE PARTICLES (r 60?m)
E/N

• The initial process for 60 ?m particle is the
  same as for 80 ?m.
• The secondary streamers can merge sooner than
  with the larger particles.

t 3.75 t 4.25 t 4.6 t 3.75
t 4.25 t 4.6
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100 - 1000 (Td) Log Scale
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ELECTRON DENSITY FOR THREE 80 ?m PARTICLES

• Electron flow envelopes the particles.
• Plasma density is larger near the particle
  surfaces.
• A wake of smaller electron density above the
  particle is due to electron flow around the
  particle.

t 3.45 t 4.2 t
4.75 ns
1012 - 6 x 1014 (cm-3) Log Scale
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PHOTOIONIZATION SOURCE FOR THREE 80 ?m PARTICLES

• Photoionization is enhanced in regions of high
  electric field.
• For two or more particles there are bursts of
  photoelectrons.
• A relay-like process results in which streamer is
  handed off between particles.

t 2.95 t 3.95 t 4.25
t 4.8 ns
109 - 7x1022 (/cm3-s) Log Scale
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STREAMER VELOCITY VS PARTICLE NUMBER AND SIZE

• Streamer velocity increases in the presence of
  dust particles.
• There exist an optimum for particle size and
  particle separation at which the streamer
  velocity is maximal.

• Particles are separated by gaps
• of 3 particle diameter

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CONCLUDING REMARKS

• The intersection of propagating streamers with
  particles not only charges the particles but can
  also significantly perturb the streamer dynamics
• Loss of charge
• Electric field enhancement
• Secondary processes.
• The interaction between the streamer electric
  field and the local (surface) electric field
  dominates the dynamics.
• The particle size and dielectric constant
  (capacitance) and conductivity modify interaction
  due to charge accumulation and shorting of field.
• Streamerparticle interactions are more complex
  for more random assemblies of particles having
  different sizes.

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